Find Density Functions of X, Y, Z Variates

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Homework Help Overview

The discussion revolves around finding the density functions of random variables derived from a given variable X, which takes on values 1, 2, 3, and 4 with equal probability. The transformations Y and Z are defined in relation to X, and participants are evaluating the correctness of the derived density functions.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to derive the probability density functions for the transformed variables Y and Z based on the given probabilities of X. They seek validation for their solutions.

Discussion Status

Some participants confirm the correctness of the original poster's solutions for parts a and b. However, the conversation shifts to personal experiences related to exams, indicating a mix of academic and social interaction without further technical exploration.

Contextual Notes

Participants mention the importance of studying various types of functions related to random variables, suggesting that there may be additional considerations or constraints in the broader context of the topic.

iHeartof12
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The random variable X assumes the values 1,2,3 and 4 with equal probability. Find the density functions of the following variates:

Attempted solutions:

X 1 2 3 4
Pr(X) 1/4 1/4 1/4 1/4

a) Y=1-2X

Y -1 -3 -5 -7
Pr(Y) 1/4 1/4 1/4 1/4

b) Z= X/(X+1)

Z 1/2 2/3 3/4 4/5
Pr(Z) 1/4 1/4 1/4 1/4

Are my solutions for parts a and b correct?
 
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Yes, this is correct.
 
Thank you. How'd your exam go today? I'm ready to get my exam over tomorrow I have a few more next week that I'm also studying for. Ahh the life of a college student. lol.
 
It went fine except for one problem that made absolutely no sense to me. Don't forget to study the pdf of a random variable of a decreasing function, not just an increasing one. There was no extra credit :( But I guess that's what you get when you can do six and he'll grade your best five.
 

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